Technical Field
Embodiments of the subject matter disclosed herein generally relate to methods and systems and, more particularly, to mechanisms and techniques for mitigating cycle-skipping in full waveform inversion (FWI).
Discussion of the Background
Seismic data acquisition and processing techniques generate a profile (image) of the geophysical structure (subsurface) of the earth. While this profile does not provide an accurate location for oil and gas, it suggests, to those trained in the field, the presence or absence of oil and/or gas. Thus, providing a high-resolution image of the subsurface is an ongoing process for the exploration of natural resources, including, among others, oil and/or gas.
During a seismic gathering process, as shown for instance in the marine case in FIG. 1, a vessel 110 tows plural detectors 112, which are disposed along a cable 114. Cable 114 and its corresponding detectors 112 are sometimes referred to, by those skilled in the art, as a streamer 116. Vessel 110 may tow plural streamers 116 at the same time. The streamers may be disposed horizontally, i.e., lie at a constant depth z1 relative to the ocean surface 118. Also, plural streamers 116 may form a constant angle (i.e., the streamers may be slanted) with respect to the ocean surface as disclosed in U.S. Pat. No. 4,992,992, the entire content of which is incorporated herein by reference. In one embodiment, the streamers may have a curved profile as described, for example, in U.S. Pat. No. 8,593,904, the entire content of which is incorporated herein by reference.
Still with reference to FIG. 1, vessel 110 may also tow a seismic source 120 configured to generate acoustic waves 122a. Acoustic wave 122a propagates downward and penetrates the seafloor 124, eventually being reflected by a reflecting structure 126 (reflector R). Reflected acoustic wave 122b propagates upward and is detected by detector 112. For simplicity, FIG. 1 shows only two paths 122a corresponding to the acoustic waves. Parts of reflected acoustic wave 122b (primary) are recorded by various detectors 112 (recorded signals are called traces), while parts of reflected wave 122c pass detectors 112 and arrive at the water surface 118. Since the interface between the water and air is well approximated as a quasi-perfect reflector (i.e., the water surface acts as a mirror for acoustic waves), reflected wave 122c is reflected back toward detector 112 as shown by wave 122d in FIG. 1. Wave 122d is normally referred to as a ghost wave because it is due to a spurious reflection. Ghosts are also recorded by detector 112, but with a reverse polarity and a time lag relative to primary wave 122b if the detector is a hydrophone. The degenerative effect that ghost arrival has on seismic bandwidth and resolution is known. In essence, interference between primary and ghost arrivals causes notches, or gaps, in the frequency content recorded by detectors.
The recorded traces may be used to image the subsurface (i.e., earth structure below surface 124) and to determine the position and presence of reflectors 126, which is associated with the detection of oil and/or gas reservoirs. Although FIG. 1 illustrates a marine streamer seismic acquisition system, an ocean bottom seismic or a land seismic acquisition system is similar to the marine seismic acquisition system in the sense that the ocean bottom seismic system has seismic sensors distributed over the ocean bottom, while the land seismic data acquisition system has seismic sensors distributed over land and seismic sources (e.g., vibrators) are moved by trucks from place to place to generate the seismic waves.
FWI is used to generate a high-resolution and high-fidelity velocity model which improves the migration results and provide direct information about the reservoir. However, because of the highly oscillatory nature of the seismic data and the inherent strong nonlinearity of the objective function, the conventional Least-Squares (LS) FWI often suffers from numerous local minimums, with a very narrow basin of convergence near a global minimum. These detrimental cycle skipping effects occur when the arrival time differences between the predicted and the recorded wave fields are larger than half a cycle of the dominant frequency of the seismic data.
To deal with these shortcomings of the FWI, frequency sweeping methods introduced by Bunks et al. 1995, (Bunks C., F. Saleck, S. Zaleski and G. Chavent, 1995, Multiscale seismic waveform inversion; Geophysics, 60, 1457-1473) and Pratt 1999 (Pratt R. G., 1999, Seismic waveform inversion in the frequency domain, part 1: Theory and verification in a physical scale model; Geophysics, 64, 888-901.) fit data from low to high frequency components to avoid cycle skipping. The success of frequency sweeping FWI strongly relies on some demanding prerequisites, including an accurate initial velocity model and sufficient low frequency components. In field data processing, seismic data below 3 to 4 Hz is often unavailable due to acquisition limitations and noise contamination. On the other hand, travel time tomography, which is often used to provide the initial velocity model for FWI, has its own limitations. Especially within or beneath the shallow velocity anomaly, limited common image gather curvatures are available for Residue Curvature Analysis based tomography. Moreover, the range of updated depth of the ray-based diving wave tomography is typically limited. As a consequence, the cycle skipping issues in FWI are still an open subject.
Thus, there is a need to develop new FWI methods that mitigate cycle-skipping.